Charge-exchange collisions of C60z+ : a probe of the ion

charge distribution

Douglas B. Cameron and Joel H. ParksRowland Institute for Science, Cambridge, MA 02142-1297, USA

Abstract

We present Paul trap measurements of charge-exchange collisions of Li, Cs and C60with C60

z+ ions (z=1-3) at thermal energies. Surprisingly, the measured charge-exchange rates for each neutral species are not proportional to the ion charge z aswould be expected for Langevin collisions involving a uniformly charged ion. Therelative rates can be reproduced by a model based on a symmetric distribution of pointcharges that are free to move on the ion surface during the neutral trajectory. Suchbehavior can be attributed to static and possibly dynamic Jahn-Teller effects in C60

z+

ions.

1. Introduction

Multiply charged C60z+ ions provide a unique opportunity to observe charge-

exchange interactions which exhibit a strong dependence on the distribution andmobility of charge on the molecular microsurface. Since the diameter of C60 (~7Å) iscomparable to the range of the ion-neutral interaction during collisions, it might beexpected that the collision dynamics depend on characteristics of the ion chargedistribution. Studies of low energy charge-exchange between C60

+ and alkali atoms [1]

and of C602+ with small molecules [2] have suggested models of a charge distribution

that included charge motion on the ion microsurface during the interaction trajectory. Asymmetric distribution of +z point charges on the C60 surface was proposed by Bohme

and co-workers [3] to describe the charge-exchange process from C60z+ ions and was

applied to experimental results of fission (dissociation) reactions with 3£z£7 by Märk

1

and co-workers [4]. This letter presents experimental results which relate the long range ion-neutral

interaction to the ion charge distribution. Our results are not expected to depend on thedetails of the curve-crossing dynamics where charge-exchange occurs. These crossingsare estimated to occur at ion-neutral separations shorter than the Langevin criticalcapture distance arising in ion-induced dipole collisions. This is in contrast to themeasurements of C2

+ fission [4] which require a model of the C60z+ ion distribution at

the point of charge separation to estimate the fission dynamics. However, both fissionand the collision interactions of C60

z+ can be described with a distribution of equidistantpoint charges on the ion surface. In addition, the collision rates obtained from ourexperiments imply that the charge distribution is free to undergo rigid rotation aboutthe C60 microsurface during the collision trajectory. The experimental implications of anonuniform charge distribution and its apparent rapid rotation during the collision arediscussed in the context of Jahn-Teller effects, previously studied for anions, cations andneutral triplet states of C60.

2. Experiment

The experimental arrangement used for these measurements has been describedelsewhere [1,5]. C60

z+ ions and C60-2mz+ fragments were loaded into a radio frequency

Paul trap by electron ionization of an effusive beam of C60 entering through an

aperture in the ring electrode. Multiply-charged ions (£ 103 ions) were produced by anelectron beam current density of ~2 mA/cm2 at ~100 eV energy for exposure times of0.5-1 s. The trap was maintained at 300 K and ions were stored within a background Hegas at pressures of ~10-4 Torr, adequate to thermalize the translational and vibrationaldegrees of freedom. [1] The ions were then exposed to a thermal beam of alkali atomsor C60 molecules that traverses the trap through two apertures in the ring electrode foran exposure interval set by a solenoid driven shutter.

Charge-exchange collisions between C60z+ ions and alkali atoms resulted in a decay of

the number of trapped ions. Previous experiments [1] demonstrated that this was theonly significant process responsible for ion decay. The trapped ion lifetime was severalminutes in the absence of neutral flux and contributed negligible loss to thesemeasurements. After exposing the trapped ions to the neutral beam for a specific timeinterval, the number of remaining ions was determined by resonantly ejecting alltrapped ions into an electron multiplier. Simultaneous measurements on ions havingdifferent charge states z could be made by trapping a range of m/z ions. This allowedan accurate determination of the decay rates of C60

z+ relative to C60+. These relative

rates eliminate the dependence on the neutral flux which, although required forabsolute rates, was found to be difficult to calibrate accurately. [1] Figure 1 displays themass spectrum of trapped ions before exposure to neutral flux. The trapped ionspectrum in Fig. (1) spans a trap parameter range of 0.21£qz£0.84 and the number of

2

ions for each species is proportional to the integrated peak signal. By performing thesemeasurements as a function of exposure interval, the relative charge-exchange rate ofeach ion species was determined.

The charge-exchange channels observed in these experiments resulted from reactions

C M C M M Li Cs Cm

zm

z60 2 60 2

160-

+-

- + ++ Æ + = , ,( ) (1)

Charge-exchange rates were extracted from the analysis of multiply-charged massspectra by comparing the measured time dependent population of each species with thesolution of a coupled set of differential equations involving collision rate parameters.The decay rate of each species was then independently determined as fit parameters tothese solutions. As an example, the decay of C60

z+ ions (z=1-3) during Li flux exposureis shown in Fig. 2. Each data point is an average of ~5 measurements and exhibitsscatter arising from statistical fluctuations. The cascade of +2 to +1 ions is clearly evidentin the initial increase of the +1 species. The experimental rates derived from exponentialfits of the decay curves shown in Fig. 2 are k1 = 1.88 sec

-1, k2 = 2.21 sec-1, k3 = 2.48 sec

-1

for z=+1, +2, +3 respectively with an uncertainty of ±15%. Note that these rates areclearly not proportional to the ion charge z.Precautions in these decay measurements was taken to ensure that the sequentialresonant ejection of different charge states with comparable mass results in quantitativeion detection. Within the trap, space charge fields couple the overlapping ion clouds ofdifferent species. As a result, the ejection of a dense inner cloud of low m/z ionsthrough a surrounding cloud of higher m/z can destabilize the outer cloud and affectthe quantitative detection of the higher m/z species. This is evident in Fig. 2 as largerscatter in the C60

+ signal at short exposure times when comparable quantities of C602+

are present. These effects were minimized by loading smaller initial quantities (

model, the neutral is attracted by a charge-induced dipole interaction which results in acapture trajectory for impact parameters less than a critical value b* determined by thecollision energy E0 and neutral polarizability a. However, the collision separation atwhich charge-exchange occurs rc is determined by the specific potential curve crossing

involved. It is useful to compare rc with b* to obtain a clearer interpretation of the

collision process. For the collision models described below, the calculated critical impactparameters were in the range b*~ 10-20 Å. The neutral-ion separation at the curvecrossing can be estimated as in Ref.[8] for collisions involving multiply charged ions atthermal energies. For collisions of C60

2+ with Li, we estimate a crossing separation ofrc~ 5-7 Å from ion center, assuming two point charges on the ion surface.

Consequently, in the present experiments, b* is sufficiently greater than rc that thecollision rates are expected to be more dependent on the ion charge distributionthrough the ion-neutral interaction than on details of the charge-exchange curvecrossing. This is in contrast to the measurements determining details of C60

z+ fission

energetics [4] and charge-exchange measurements of C602+ with C60

at high collisionenergies [9] both of which are more strongly dependent on the details of the chargedynamics at the point of charge-exchange. As a result of these considerations, thefollowing analysis will concentrate on characterizing the dependence of the long rangecharge-induced dipole interaction on the ion charge distribution. Decay ratemeasurements will be compared with calculated collision rates derived from differentassumptions of this charge distribution.

In the case of multiply-charged ions, the Langevin model predicts collision ratesproportional to ion charge z. However, as indicated in Fig. 2, the measured relativedecay rates of C60

3+, C602+ and C60

+ are clearly inconsistent with this simple Langevin

model. Considering that the diameter of C60z+ (~7Å) is only a factor of 2-3 smaller than

the critical impact parameter b*, we propose that this departure from the Langevinmodel arises from an increased sensitivity to the nonuniformity of the ion chargedistribution. As will be discussed more thoroughly below, a nonuniform ion chargedistribution can arise from Jahn-Teller distortions of the icosahedral ion structure.Consequently, an analysis of the collision process will require a more detaileddescription of the ion charge distribution.

In many environments C60 behaves as a delocalized p-electron system with a

polarizability comparable to that of a metal sphere of the same diameter [10]. If C60z+ is

modeled as a rigid metallic sphere of 3.55 Å radius, during the collision it becomespolarized by the fields of the induced dipole giving rise to an induced charge which isnonuniformly distributed on the microsurface. However, this nonuniformity wascalculated and found to produce insignificant deviations from the Langevin crosssections (

configurations for a set of like charges on the surface of a sphere have been consideredpreviously [11] and recently applied to charge-exchange [3], electrochemical reduction[12] and dissociation [4] of C60

z+. Only the simpler geometries for 2 charges at oppositeends of a diameter, and 3 charges at the vertices of an equilateral triangle will berelevant to our analysis of doubly and triply ionized species. We present the followingmodifications of the Langevin model which involve point charge approximations of thecharge distribution. Although each distribution is based upon a minimal energyconfiguration, these alternative models cover the two extremes of fixed and mobilecharges.

3.1 Stationary Charges

In contrast to the metallic model, we assume that the z charges are localized to pointson the C60

z+ surface. The collision model based on this distribution was evaluated byexplicitly integrating the trajectory to determine the cross section. To accomplish this,forces were computed for the charge-induced dipole configuration as shown in Fig.3 forz=3. Charges on C60

3+ with radius R induce a dipole p on the neutral particle of

polarizability a. The induced dipole is expressed in terms of the net field from the pointcharges, p = aE = a 3 E

i . The potential energy V is expressed by

Vp E e

r

n n

r r

i j

i jii= -

◊= - +

( )

È

Î

ÍÍÍ

˘

˚

˙˙˙

ÂÂ2 2

12

4 2

a (2)

and the force Fi on m due to the charge located at ri is given by

F n e

r

n n

r r r ri i

i j

i j i jii= +

È

Î

ÍÍÍ

˘

˚

˙˙˙

-ÂÂa 24 3 2 3 2

1 3 1 (3)

where ni is a unit vector in the direction of ri. The total force is then given by

F Fii

= Â and the resulting ion rotation follows from the torque equation,

T Ri

i x F Fii

= = ÂÂ .To determine the cross sections for each charge state z=1-3, a particular orientation of

the charge distribution was selected and the critical impact parameter b*wasdetermined from the outcome of successive trajectories which varied the impactparameter. This evaluation was repeated for random selections of orientation and initialvelocity in a Monte Carlo fashion to average the cross section over all orientations and

5

the velocity distribution of the neutral beam. This average cross section is then

related to the collision rate k v d dz z v z v= ( )Ú = Ú

• •s s

0 0F F where d F

v is the neutral

flux for atoms with speeds between v and v+dv. It is essential to point out here that rotational averaging of the ion charge

distribution and the resulting charge-neutral interaction will not occur during thecollision trajectory of alkali atoms or C60 since the rotational period of ~20 ps at 300K isa factor of ~30 longer than the collision duration for Li, and a factor of ~3 for C60.

3.2 Mobile Charges

In this case, the charges are considered sufficiently mobile for the distribution tomaintain an orientation determined by the induced dipole. Such a model is based on theassumption that the net torque exerted by the induced dipole on the charges is capableof maintaining the distribution of point charges in the lowest energy configuration. Inthis configuration, one charge is oriented nearest the dipole throughout the neutraltrajectory and the remaining charges are positioned to minimize the repulsive energybut otherwise free to rotate about the collision line of centers. In this orientation, the netforce is a central force so that the net torque vanishes and calculation of the collisioncross section reduces to the solution of a quartic equation which can be performedwithout the need for Monte Carlo methods. However, the calculations were performedboth ways as a check on the Monte Carlo asymptote, and very close agreement wasfound.

4. Results and Discussion

The relative rates k z

/ k 1 for Li and Cs collisions with C60

z+ are compared in Fig. 4.

Rates calculated with the stationary charge model are observed to agree closely withthose calculated by the Langevin model. This was found to be the case even for theabsolute rates with different z. This is a consequence of averaging over randomorientations which yields an effective spherical charge distribution. In general, anymodel relying on a stationary charge distribution will approach the Langevin resultafter such averaging over random orientations. However, the experimentalmeasurements are in sharp disagreement with both these calculations.

Relative rates for the mobile charge model are also shown in Fig. 4 and thesecalculated rates display close agreement with experimental results. Collisions of Li andCs with C58

z+, C56z+ fragments demonstrate similar agreement with the mobile model

calculations. Charge-exchange collisions of C60z+ with neutral C60 were also measured.

It was observed that the charge-exchange of C582+ with C60 resulted in equal product

densities of C60+ and C58

+ confirming that stable products are formed in these

collisions between heavy particles. In addition, the symmetric exchange of C60+ with

6

C60 was observed to occur without loss of C60+ so that only the loss rates for C60

3+ and

C602+ could be determined. The ratio of these rates was measured to be á k 3 / k 2 é =

1.38±0.08 and the mobile charge model yields a ratio of 1.37, in close agreement withmeasurement. It is evident that motion of the charge distribution during the trajectoryplays an essential role in the physics of this collision process and that a nonuniformcharge distribution alone is not sufficient to explain this phenomena.

As shown in Fig. 4, both measurements and mobile model calculations exhibit relativerates only fractionally larger than unity, which suggests that the single charge nearestthe neutral during the trajectory effectively determines the collision rate. The absoluterates calculated for Li collisions with the mobile charge model are larger than theLangevin rates by a factor of 2.1 for C60

+, 1.3 for C602+ and 1.1 for C60

3+, and similarresults were found for Cs. This result is expected as the multiply charged ions moreclosely approximate a uniform charge distribution with increasing z. These calculationsare consistent with previous measurements [1] of alkali charge-exchange with C60

+

which indicated absolute rates in excess of the Langevin model by a factor of 2-3.Bohme [2,13] also measured occasional ion-neutral collision rates larger than Langevinrates for collisions of C60

+ and C602+ with several organic species.

Delocalized charges on the C60z+ ion surface have been neglected in our calculations.

Dielectric screening by these charges would reduce the fields at the position of theneutral leading to a smaller induced dipole and as a result slower collision rates. In thestationary charge model, the average over random orientations will tend to averageout screening effects in the relative rates. However, in the mobile charge model for z=1-3, only the closest charge contributes significantly to the induced dipole, so that theeffect of screening will be roughly independent of z. In this case, the relative rateanalysis depending on rate ratios would be insensitive to the presence of screening.Furthermore, C60

z+ fission measurements [4] indicate that screening effects wereobserved only for z$ 6.

It is also important to point out that the charge-exchange collisions studied here withz>1 occur without an energy barrier imposed by coulomb repulsion [2,3]. Theestimated ion-neutral separation at the charge-exchange curve crossing of rc~ 5-7 Å andthe neutral ionization potentials of Cs (3.9 eV), Li (5.4 eV) and C60 (7.6 eV) result in an

exothermic process which probably leaves the C60(z-1)+ ion in an excited electronic

state.The close agreement observed between the theoretical model and measured collision

rates is surprising since the ability for charge to freely move about on the ion surfacewould seem to be inconsistent with the presence of a nonuniform charge distribution.However, such a model of the charge dynamics becomes quite plausible uponconsidering the consequences of both static and dynamic Jahn-Teller effects in C60

z+.Recent ab initio calculations have shown that both positive [14] and negative [15] ions ofC60 with open electronic shells undergo static Jahn-Teller distortions which lower theicosahedral symmetry of the neutral molecule. These distortions are predicted to

7

introduce changes in the bond lengths and associated charge distributions near anequator of the molecular cage. The ion models introduced here which treat pointcharges confined to the spherical surface may be considered as a simple representationof these distortions. Dynamic Jahn-Teller effects have been indicated in photoemissionmeasurements [16] of C60

- and also as the basis for the weak temperature dependenceof electron paramagnetic resonance (EPR) spectra of triplet state C60 [17-19]. The EPRlinewidth variation with temperature is characteristic of a rotation of the symmetry axisabout the direction of the magnetic field. This observation is interpreted to result fromrapid (~10-14 - 10-13 s) tunneling [19] among nearly degenerate vibronic statesassociated with different symmetry axes. In the case of C60

z+ collisions, a similartunneling among states with different axes of molecular symmetry could reorient thecharge inhomogeneity during the collision trajectory. Such a pseudorotation of thecharge distribution would provide the apparent charge mobility suggested by ourcollision model. Further investigations are planned to detect the presence of dynamicJahn-Teller effects in collisions by measuring the dependence of the collision rates onthe vibrational temperature of trapped C60

z+ over a range of 10 to 300K.

To summarize, charge-exchange collisions of C60z+ with both alkali atoms and C60 are

observed to occur with rates which are relatively insensitive to the charge state. Thisresult contradicts calculations based upon a uniform charge distribution including thestandard Langevin model. A theoretical model which closely predicts measurements ofthe relative rates incorporates an array of point charges on the C60

z+ surface toapproximate the non-uniform distribution. In addition, the model includes the propertyof charge mobility which allows the distribution to reorient during the collisiontrajectory. These characteristics of charge localization and mobility, although seeminglycontradictory, are both required in the collision model to describe experimental results.Jahn-Teller effects including distortion of the ion charge distribution as well as apseudorotation of this distribution yield a plausible basis for the physics characterizedby the model.

Acknowledgement

We would like to thank Michael Burns, Mordechai Rokni and Abraham Szökefor relevant discussions during the progress of this work. This research was fullysupported by The Rowland Institute for Science.

8

References

[1] S. Pollack, D. Cameron, M. Rokni, W. Hill, J. H. Parks, Chem. Phys. Letters 256 (1993) 473.

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[6] P. Langevin, Ann. Chim. Phys. 5 (1905) 245 and an English translation whichappears in E. W. McDaniel, Collision Phenomena in Ionized Gases (Wiley, NewYork, 1964), p. 701.

[7] G. Gioumousis and D. P. Stevenson, J. Chem. Phys. 29 (1958) 294.

[8] A. Salop and R. E. Olson, Phys. Rev. A13 (1976) 1312.

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[11] H. A. Munera, Nature 320 (1986) 597.

[12] R. S. Ruoff, P. L. Boulas, K. M. Kadish and Y. Wang, Electrochemical Soc. Proc. 95-10 (1995) 287.

[13] G. Javahery, H. Wincel, S. Petrie and D. K. Bohme, Chem. Phys. Letters 204 (1993) 467.

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10

Figure Captions

Figure 1. The mass spectrum of trapped C60z+ and associated fragments are shown.

Ions are loaded into the trap by e-beam ionization of neutral C60 and

the spectrum is detected by resonant ejection of the ions into an electron

multiplier.

Figure 2. The decay curves for charge-exchange of C60z+ with Li are

shown for z=1 by filled circles, z=2 by filled squares and z=3 by filled

triangles. The solid curves are determined by parameter fits of the decay

rates k1, k2 and k3 shown next to curve. The data points were obtained

by integrating the mass spectrum peaks of C60z+ for each charge state z

at each Li exposure time.

Figure 3. The model geometry used to describe the interaction of C603+

having mass M with a neutral species of mass m and polarizability a is

shown. Point charges are positioned on the ion microsurface at radii Ri

and angular separations which minimize the repulsive Coulomb

interaction. The interaction potential between the point charges and the

induced dipole moment, p, is defined in Eq.(2).

Figure 4. A plot of experimental ratios of decay rates for multiply-charged

ions is compared with calculations based on different models of the ion

charge distribution. The data indicated by filled circles refer to Li measurements

and open circles to Cs measurements of C60z+ decay rates. Several decay

measurements for fragments C56z+ and C58

z+ are also shown. Calculated

20

ratios indicated by open circles refer to the Langevin model, filled (open)

squares to Li (Cs) decay in the stationary charge model and filled (open)

triangles to Li (Cs) decay in the mobile charge model. Symbols refer to each individual

charge state but are offset from the x-axis marker for clarity. Dashed lines are guides

for the eye indicating trends of the model calculations.

21

Figure 1

Figure 2

Figure 3

Figure 4